The expression “ultra-brief laser pulse” is intended to mean a picosecond pulse (duration of between about 0.1 and 100 ps) or femtosecond pulse (duration of less than or equal to 100 fs=0.1 ps). The durations are understood to be at mid-height of the intensity profile. These pulses necessarily exhibit a relatively wide spectral band, in a manner well known per se.
Ultra-brief laser pulses exhibit numerous scientific and technological applications; they can be amplified up to energies of several
Joules and form beams (“pulsed beams”) whose diameter ranges from a few millimeters to several centimeters as a function, in particular, of their power.
Generally, the temporal properties of the electromagnetic field of a pulsed beam can vary spatially or, equivalently, the spatial properties can depend on time. For example, the pulse duration can depend on the position (x,y) in the beam (hereinafter, unless indicated otherwise, consideration will always be given to a beam propagating in a “z” direction, the “x”, “y” and “z” axes forming a right-handed orthonormal reference frame).
When such a dependency exists, the field E(x,y,t) cannot be cast into the form E(x,y,t)=Et(t)·EES(x,y), where Et(t) is a function of time and EES(x,y) a function of space. The beam is then said to exhibit spatio-temporal coupling (“STC” standing for “Space-Time Coupling”).
Spatio-temporal couplings can lead in particular to a distortion, illustrated with the aid of FIGS. 1A and 1B, of the intensity front of a pulsed beam. The electromagnetic energy of an ultra-brief pulsed beam is, in the ideal case, distributed in a very slender disk (FIG. 1A) of diameter D and of thickness cT, where c is the speed of light and T the duration of the pulse; in the example of FIG. 1A, D=8 cm and cT=10 μm, thus corresponding to a pulse duration of about 33 fs. In order to maximize the luminous intensity obtained at the focus, this generally being desired, this disk must be as “flat” as possible. To characterize this spatial distribution of the energy, one speaks of the “intensity front” of the laser (not to be confused with the “wavefronts”, which depend on the wavelength).
In practice, and in particular in the case of high-power lasers with large beam diameter, the intensity fronts might not be plane, but distorted as illustrated in FIG. 1B. Consequently, the peak of the pulse may be attained at different instants in the various points of the cross section of the beam in the (x,y) plane, and the pulse duration may also vary from one point to another.
Other spatio-temporal types of coupling are also possible, such as for example a rotation of the wavefronts over time. For a general account of the theory of spatio-temporal couplings, refer to the article by S. Akturk et al. “The general theory of first-order spatio-temporal distortions of Gaussian pulses and beams, Optics Express Vol. 13, No. 21, pages 8642-8661.
Methods for measuring these couplings have been proposed, but they remain limited in their performance and complex to implement, hence they are not very widespread. The “SPIDER-2D” technique arises out of the “SPIDER” scheme (standing for “Spectral Phase Interferometry for Direct Electric Field Reconstruction”), introduced in 1998 for measuring the temporal structure of an ultra-brief pulse at a point in space. It combines spectral-shift interferometry (standard SPIDER technique) and spatial-shift interferometry to reconstruct the spectral phase φ(x,y,ω) along a spatial direction (ω being the angular frequency, related to the wavelength λ by the relation λ=2πc/(ω). In practice, this technique consists in acquiring an image of an interferogram on the sensor of a CCD camera; the dimensions of this image correspond on the one hand to the frequency ω, and on the other hand to a spatial coordinate. This spatial coordinate may be either the x coordinate or the y coordinate of the (x,y) plane perpendicular to the direction of propagation of the beam.
This technique requires a complex setup to produce several replicas of the initial beam and manipulate them with the aid, inter alia, of a nonlinear crystal. Consequently, it is difficult and expensive to implement. Furthermore, as one of the coordinates of the interferogram corresponds to a spatial coordinate transverse to the beam, this technique allows only the characterization of relatively small beams, of smaller diameter than that of the CCD sensor of the camera (typically 1 cm or less). In the case of beams of larger diameter (for example, issuing from a high-power source), it is necessary to reduce the size thereof by means of a telescope, which is liable to induce spurious spatio-temporal couplings. Another drawback is that the principle of the technique makes it necessary to perform the measurement according to a single transverse spatial coordinate, x or y.
The so-called “STRIPED FISH” technique utilizes a measurement of the spatial interferences between the beam to be characterized and a so-called reference beam, doing so for a set of frequencies in the spectrum of the beam to be characterized. The reference beam must exhibit a spectrum which encompasses that of the beam to be characterized, and have a phase φ0(x,y,ω) that is known at every point and for all frequencies. The interferograms make it possible to compare, for a set of frequencies ωi, the phase φ(x,y,ω) of the beam to be characterized, with the known phase φ0(x,y,ω) of the reference beam. This technique is much simpler to implement than SPIDER-2D, and a single measurement makes it possible to characterize the beam in the two transverse directions x and y. On the other hand, the diameter of the beam must be small relative to the size of the CCD sensor used to acquire the images of the interferograms; this beam size limitation is still more constraining than in the case of SPIDER-2D.
The closest prior art consists of a third technique, called “SEA TADPOLE”, which is described in patent U.S. Pat. No. 7,817,282 and in the article by Bowlan et al “Directly measuring the spatio-temporal electric field of focusing ultrashort pulses” Optics Express, 15 10219 (2007). As illustrated in FIG. 2, this technique consists in collecting the light at various points of the beam to be characterized FL with a monomode fiber F1. This collection of light in the unknown beam can be done either at the focus of a focusing optic, or on an unfocused beam. An auxiliary beam FA, of spectral phase φaux(ω), is injected into a second monomode fiber F2. The exit ends of the two fibers are placed side by side; a convergent lens L1 deviates the beams exiting the fibers in such a way that they overlap spatially, thus producing spatial interferences which are resolved spectrally with the aid of a spectrometer SPM comprising a diffraction grating RD and a cylindrical lens L2 (the reference FE identifies the entry slit of the spectrometer, perpendicular to the direction of dispersion of the latter). An interferogram S(ω,X) is thus obtained, where X is the spatial coordinate normal to the direction of dispersion of the spectrometer, an image of which is acquired by virtue of a sensor of CCD type, identified by the reference CI.
It is possible to use this interferogram to determine the spectral phase difference between the pulses injected into the two fibers. The intensity S(ω,X) measured on the CCD sensor of the spectrometer as a function of ω and X is given by:S(ω,X)=Saux(ω)+Sinc(ω)+2√{square root over (Saux(ω)Sinc(ω))}{square root over (Saux(ω)Sinc(ω))}cos(2ω sin θX/c+φinc(ω)−φaux(ω))  (1)
where Saux and Sinc, are respectively the spectral intensities of the auxiliary pulse and pulse to be characterized which are injected into the fibers, φaux and φinc their spectral phases at the fiber exit, θ is the half-angle between the beams, θ=a tan(d/(2L)), where d is the distance between the fibers and L the distance between fiber exits and detector. An exemplary interferogram S(ω,X) is presented in FIG. 3A.
The interference term in equation (1), which will be denoted by J(ω,X), contains information on the phase difference Δφ(ω)=φinc−φaux between the pulses which have been collected by the two fibers. To extract this information, the procedure used consists in calculating the Fourier transform of this function with respect to the variable X (TF1D: one-dimensional Fourier transform). As shown in FIG. 3B, this Fourier transform comprises three components in the (ω, k) plane. The central component, which comprises only low frequencies, corresponds to the term Saux+Sinc in equation (1). The other two components correspond to the two complex exponentials of the following decomposition of the interference term:J(ω,X)=√{square root over (Saux(ω)Sinc(ω))}{square root over (Saux(ω)Sinc(ω))}(eiφ+e−iφ)  (2)
with φ=2ω sin θ·X/c+φinc(ω)−φaux(ω).
If a single of these components is selected, for example by multiplying the Fourier transform by an appropriate filter, in particular supergaussian, and if an inverse Fourier transform is performed, the following function is obtained:{tilde over (J)}(ω,X)=√{square root over (Saux(ω)Sinc(ω))}{square root over (Saux(ω)Sinc(ω))}eiφ  (3)
the phase φ of which equals:
φ=2ω sin θ·X/c+φinc(ω)−φaux(ω)=φgeo(ω)+Δφ(ω).
The first term φgeo(ω) (“geometric”) is simply induced by the angle used to generate spatial fringes. The second term Δφ(ω)=φinc(ω)−φaux(ω) represents the spectral phase difference between the beams on exit from the two fibers, that is to say between a point of the beam to be characterized (corresponding to the entry end of the first fiber) and the auxiliary beam. One therefore proceeds in the following manner:                the interferogram S(ω,X) is measured and the processing hereinabove is performed for a given position (x0,y0) of the first fiber in the beam to be characterized. From this is deduced φ0=2ω sin θ·X/c+φ(ω,x0,y0)−φaux(ω);        the interferogram S(ω,X) is thereafter measured and the processing hereinabove is performed for a set of position (xi,yi) of the fiber 1 in the beam to be characterized. A phase φi=2ω sin θ·X/c+φ(ω,xi,yi)−φaux(ω) is deduced therefrom. The phase φ0 measured during the first shot is systematically subtracted. We thus obtain Δφi(ω)=φ(ω,xi,yi)−φ(ω,x0,y0). This phase is independent of X, and can be averaged along this axis so as to improve the signal/noise ratio. By proceeding thus, all the points of the beam are therefore compared with the point (x0,y0), using the auxiliary beam as intermediary.        It is thereafter possible to perform a measurement of SPIDER or FROG (standing for “Frequency Resolved Optical Gating”) type at the point (x0,y0), to determine the dependency of φ(ω,x0,y0) versus frequency (ω). We then have all the information required in order to reconstruct the field E(xi,yi,t) of the laser beam, by a Fourier transform with respect to ω, this to within a phase term, which term is almost independent of ω and which, as will be discussed further on, is introduced by the optical fibers.        
This technique requires only an inexpensive setup that is relatively simple to achieve, and can be applied to beams of large size. On the other hand, as the phase is determined point by point, the characterization of a beam requires a large number of laser shots. This results in a significant acquisition time and sensitivity to temporal fluctuations and drifts of the laser source, to vibrations and to defects of positioning of the entry ends of the optical fibers.
Another limitation of the SEA TADPOLE technique consists in the fact that the optical fibers introduce random phase fluctuations, which cannot be measured (this point was briefly mentioned above). This implies that the electric field of the beam E(x,y,t) cannot be reconstructed completely, but only except for an unknown phase term φfluct(xi, yi, ω). If the information thus obtained makes it possible to determine, for example, the intensity fronts (by virtue of the assumption, confirmed by experiment, that φfluct depends does not depend on the frequency ω), the phase fronts cannot be reconstructed.